Limp and limpid have very different meanings.
Limp as an adjective describes a kind of structural (physical) weakness; it means loose or floppy, not stiff or rigid, like a noodle, wet cloth, or a very tired person:
After digging all day, his arms hung limp at his sides; they were so worn out.
Without wind, the flag hung limp from the flagpole.
And yes, the phrase, hang limp, is a real English expression!
Limp as a verb or noun describes the way that people or animals walk when they have a weakness in one leg or one side—with uneven movements, not smoothly:
John limped/had a limp, after he was hit by the car.
John had a limp, after he was hit by the car.
Vehicles can also “limp,” when they are damaged and do not move smoothly in a straight line.
Limpid, in contrast, is a good quality, meaning “perfectly clear,” or lucid. Often, eyes or water are described as limpid (though it’s a bit of a cliché):
Gina loved to look into the limpid pools of his clear blue eyes.
The word limpid usually appears in literature, and not so much in everyday conversation.